So, recently while I was revisiting rotational dynamics, I came across this question: A rod AB of length L stands vertically on a horizontal floor and its end B is at height L. Now the end B starts falling down because of some slight disturbance and end A does not slip. Calculate the speed with which the end B hits the ground.
See, this question can be easily done by applying mechanical energy conservation. Since the end A is not moving there must be enough friction there, even then we can easily apply energy conservation because the point where friction acts (end A) does not displace, hence work done by friction is zero. But why can't we apply angular momentum conservation about the centre of mass of that rod as there won't be any net torque about CM? (As I said, the point where friction acts doesn't move so its work is zero, and in case of gravity, the torque due to weight will be zero as we are considering our axis to pass through CM.)